Comparison of the Extended and Unscented Kalman Filters for Angles Based Relative Navigation

International Journal of Navigation and Observation

Gross

et al. 2011

Using an Unscented Kalman Filter (UKF) as the nonlinear estimator within a Global Positioning System/Inertial Navigation System (GPS/INS) sensor fusion algorithm for attitude estimation, various methods of calculating the matrix square root were discussed and compared. Specifically, the diagonalization method, Schur method, Cholesky method, and five different iterative methods were compared. Additionally, a different method of handling the matrix square root requirement, the square-root UKF (SR-UKF), was evaluated. The different matrix square root calculations were compared based on computational requirements and the sensor fusion attitude estimation performance, which was evaluated using flight data from an Unmanned Aerial Vehicle (UAV). The roll and pitch angle estimates were compared with independently measured values from a high quality mechanical vertical gyroscope. This manuscript represents the first comprehensive analysis of the matrix square root calculations in the context of UKF. From this analysis, it was determined that the best overall matrix square root calculation for UKF applications in terms of performance and execution time is the Cholesky method.

Section: Introductionmentioning

confidence: 99%

Evaluation of Matrix Square Root Operations for UKF within a UAV GPS/INS Sensor Fusion Application

International Journal of Navigation and Observation

Gross

et al. 2011

“…1, K is the Kalman gain matrix, which is calculated from the equations of a nonlinear Kalman filter. A common simplification used in many applications [12,17,29,30] is that the process and measurement noise are additive [31], as in…”

Section: Problem Formulationmentioning

confidence: 99%

“…Kandepu et al [11] presented the same conclusions through four different simulation studies of the following problems: Van der Pol oscillator, estimation in an induction machine, state estimation of a reversible reaction, and a solid oxide fuel cell combined gas turbine hybrid system. Stastny et al [12], Akin et al [13], Chowdhary and Jategaonkar [14], Giannitrapani et al [15], and Kim et al [16] concluded that the UKF achieves slightly better performance than the EKF within applications of angles-based navigation, state estimation of induction motors, aerodynamic parameter estimation, spacecraft localization using angle measurements, and spiraling ballistic missile state estimation, respectively. Saulson and Chang [17] and LaViola [18] found insignificant differences in the performance between the EKF and UKF for the ballistic missile tracking problem and for estimation of quaternion motion for human tracking, respectively.…”

Section: Introductionmentioning

confidence: 96%

Sensitivity Analysis of Extended and Unscented Kalman Filters for Attitude Estimation

Journal of Aerospace Information Systems

Gross

et al. 2013

The extended Kalman filter (EKF) and unscented Kalman filter (UKF) for nonlinear state estimation with both additive and nonadditive noise structures are presented and compared. Three different Global Positioning System (GPS)/inertial navigation system (INS) sensor fusion formulations for attitude estimation are used as case studies for the nonlinear state estimation problem. A diverse set of actual flight data collected from research unmanned aerial vehicles was used as empirical data for this study. Roll and pitch estimation results were compared with independent measurements from a mechanical vertical gyroscope to evaluate the performance. The performance of the EKF and UKF is compared in terms of noise assumptions, covariance matrix tuning, sampling rate, initialization error, GPS outages, robustness to inertial measurement unit bias and scale factors, and linearization. Similar sensitivity for this GPS/INS attitude estimation problem was found between the EKF and UKF for most cases. Small differences were seen between EKF and UKF for initialization error and GPS outages: the UKF was found to be more robust to inertial measurement unit calibration errors, and the EKF was determined to be more computationally efficient.

“…However, other researchers found that the UKF only outperformed the EKF for GPS/INS sensor fusion under large initialization errors [9,[31][32][33]. Slight performance advantage of the UKF over the EKF was reported for angles-based navigation [34], GPS/INS position estimation [35], state estimation of induction motors [36], and aerodynamic parameter estimation [37]. Some studies of the problems of aircraft attitude estimation [6,8], ballistic missile tracking [38] and quaternion motion for human tracking [39] found insignificant differences in EKF and UKF performance.…”

Section: Introductionmentioning

confidence: 99%

An Analytical Approach for Comparing Linearization Methods in EKF and UKF

International Journal of Advanced Robotic Systems

Napolitano

2013

The transformation of the mean and variance of a normally distributed random variable was considered through three different nonlinear functions: sin(x), cos(x), and xk, where k is a positive integer. The true mean and variance of the random variable after these transformations is theoretically derived within, and verified with respect to Monte Carlo experiments. These statistics are used as a reference in order to compare the accuracy of two different linearization techniques: analytical linearization used in the Extended Kalman Filter (EKF) and statistical linearization used in the Unscented Kalman Filter (UKF). This comparison demonstrated the advantage of using the unscented transformation in estimating the mean after transforming through each of the considered nonlinear functions. However, the variance estimation led to mixed results in terms of which linearization technique provided the best performance. As an additional analysis, the unscented transformation was evaluated with respect to its primary scaling parameter. A nonlinear filtering example is presented to demonstrate the usefulness of the theoretically derived results